### Abstract

In this paper, we consider three versions of semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the makespan. In the first version, we assume that the total size of jobs with lower hierarchy is given and we get the tight bound (Formula presented.). In the second one, assume that the total size of jobs in each hierarchy is given and we get the tight bound (Formula presented.). In the third one, we assume that the total size of jobs with lower hierarchy is known in advance and a buffer of size K is given to store at most K jobs temporarily. We propose an optimal algorithm with competitive ratio (Formula presented.) using K=1 and show that a bigger buffer size is not helpful.

Original language | English |
---|---|

Pages (from-to) | 873-881 |

Number of pages | 9 |

Journal | International Journal of Computer Mathematics |

Volume | 92 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 4 2015 |

### Fingerprint

### Keywords

- competitive ratio
- hierarchical constraint
- scheduling problem
- semi-online

### ASJC Scopus subject areas

- Applied Mathematics
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*International Journal of Computer Mathematics*,

*92*(5), 873-881. https://doi.org/10.1080/00207160.2014.922682

**Online hierarchical scheduling on two machines with known total size of low-hierarchy jobs.** / Chen, Xin; Ding, Ning; Dósa, G.; Han, Xin; Jiang, He.

Research output: Contribution to journal › Article

*International Journal of Computer Mathematics*, vol. 92, no. 5, pp. 873-881. https://doi.org/10.1080/00207160.2014.922682

}

TY - JOUR

T1 - Online hierarchical scheduling on two machines with known total size of low-hierarchy jobs

AU - Chen, Xin

AU - Ding, Ning

AU - Dósa, G.

AU - Han, Xin

AU - Jiang, He

PY - 2015/5/4

Y1 - 2015/5/4

N2 - In this paper, we consider three versions of semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the makespan. In the first version, we assume that the total size of jobs with lower hierarchy is given and we get the tight bound (Formula presented.). In the second one, assume that the total size of jobs in each hierarchy is given and we get the tight bound (Formula presented.). In the third one, we assume that the total size of jobs with lower hierarchy is known in advance and a buffer of size K is given to store at most K jobs temporarily. We propose an optimal algorithm with competitive ratio (Formula presented.) using K=1 and show that a bigger buffer size is not helpful.

AB - In this paper, we consider three versions of semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the makespan. In the first version, we assume that the total size of jobs with lower hierarchy is given and we get the tight bound (Formula presented.). In the second one, assume that the total size of jobs in each hierarchy is given and we get the tight bound (Formula presented.). In the third one, we assume that the total size of jobs with lower hierarchy is known in advance and a buffer of size K is given to store at most K jobs temporarily. We propose an optimal algorithm with competitive ratio (Formula presented.) using K=1 and show that a bigger buffer size is not helpful.

KW - competitive ratio

KW - hierarchical constraint

KW - scheduling problem

KW - semi-online

UR - http://www.scopus.com/inward/record.url?scp=84922433726&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922433726&partnerID=8YFLogxK

U2 - 10.1080/00207160.2014.922682

DO - 10.1080/00207160.2014.922682

M3 - Article

VL - 92

SP - 873

EP - 881

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 5

ER -